Question

three numbers are in gp.whose sum is 14 and their product 64.find the numbers.
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Answer 1

Answer:

Explanation:

Let three numbers in G.P=a,ar,ar2

Sum of three number=14

a+ar+ar2=14 ……..(1)

Sum of squares of number=84

a2+a2r2+a2r4=84

Squaring equation (1) both sides

a2+a2r2+a2r4+2a2r+2a2r3+2a2r2=196

84+2a2r(1+r2+r)=196

2a2ra14​=196−84

2ar14=112

a=14×2r112​=r4​

r4​+4+4r=14

4+4r+4r2=14r

4r2−10r+4=0

2r2−5r+2=0

r=45±25−16

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r=45±3​

=2,21​

r=2,a=2; r=21​,a=8

Three terms: 2,4,8

Three terms: 8,4,2

∴ Three terms are: 2,4,8.

Answer 2

Answer:

Answer is in the attachment